Time-inconsistent optimal control problem with random coefficients and stochastic equilibrium HJB equation

Haiyang  Wang; Zhen Wu

doi:10.3934/mcrf.2015.5.651

Article Contents

2015, Volume 5, Issue 3: 651-678. Doi: 10.3934/mcrf.2015.5.651

This issue Previous Article Optimal control problems of forward-backward stochastic Volterra integral equations Next Article Constrained nonsmooth utility maximization on the positive real line

Time-inconsistent optimal control problem with random coefficients and stochastic equilibrium HJB equation

Haiyang Wang^1, and
Zhen Wu^1,

1.
School of Mathematics, Shandong University, Jinan 250100

Received: January 31, 2014

Revised: June 30, 2014

Published: August 2015

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Abstract

In this paper, we study a class of time-inconsistent optimal control problems with random coefficients. By the method of multi-person differential games, a family of parameterized backward stochastic partial differential equations, called the stochastic equilibrium Hamilton-Jacobi-Bellman equation, is derived for the equilibrium value function of this problem. Under appropriate conditions, we obtain the wellposedness of such an equation and construct the time-consistent equilibrium strategy of closed-loop. Besides, we investigate the linear-quadratic problem as a special and important case.

Keywords:

Time inconsistency,
multi-person differential games,
equilibrium strategy,
equilibrium HJB equation,
stochastic partial differential equations,
linear-quadratic problem.

Mathematics Subject Classification: Primary: 93E20; Secondary: 60H15.

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